Displaying similar documents to “On 2-distributions in 8-dimensional vector bundles over 8-complexes”

On 4-fields and 4-distributions in 8-dimensional vector bundles over 8-complexes

Martin Čadek, Jiří Vanžura (1998)

Colloquium Mathematicae

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Let ξ be an oriented 8-dimensional spin vector bundle over an 8-complex. In this paper we give necessary and sufficient conditions for ξ to have 4 linearly independent sections or to be a sum of two 4-dimensional spin vector bundles, in terms of characteristic classes and higher order cohomology operations. On closed connected spin smooth 8-manifolds these operations can be computed.

On the functorial prolongations of principal bundles

Ivan Kolář, Antonella Cabras (2006)

Commentationes Mathematicae Universitatis Carolinae

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We describe the fundamental properties of the infinitesimal actions related with functorial prolongations of principal and associated bundles with respect to fiber product preserving bundle functors. Our approach is essentially based on the Weil algebra technique and an original concept of weak principal bundle.

Natural transformations between T²₁T*M and T*T²₁M

Miroslav Doupovec (1991)

Annales Polonici Mathematici

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We determine all natural transformations T²₁T*→ T*T²₁ where T k r M = J 0 r ( ℝ k , M ) . We also give a geometric characterization of the canonical isomorphism ψ₂ defined by Cantrijn et al.

Continuity of projections of natural bundles

Włodzimierz M. Mikulski (1992)

Annales Polonici Mathematici

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This paper is a contribution to the axiomatic approach to geometric objects. A collection of a manifold M, a topological space N, a group homomorphism E: Diff(M) → Homeo(N) and a function π: N → M is called a quasi-natural bundle if (1) π ∘ E(f) = f ∘ π for every f ∈ Diff(M) and (2) if f,g ∈ Diff(M) are two diffeomorphisms such that f|U = g|U for some open subset U of M, then E(f)|π^{-1}(U) = E(g)|π^{-1}(U). We give conditions which ensure that π: N → M is continuous. In particular,...

On topological invariants of vector bundles

Zbigniew Szafraniec (1992)

Annales Polonici Mathematici

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Let E → W be an oriented vector bundle, and let X(E) denote the Euler number of E. The paper shows how to calculate X(E) in terms of equations which describe E and W.

On special types of nonholonomic 3 -jets

Ivan Kolář (2012)

Archivum Mathematicum

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We deduce a classification of all special types of nonholonomic 3 -jets. In the introductory part, we summarize the basic properties of nonholonomic r -jets.